Minimum radius for radial turnaround with bounded proper acceleration ($g_{\mathrm{hover}}=GM/[r^2\sqrt{1-2GM/(c^{2}r)}]$)

For radial motion in Schwarzschild spacetime, $a^r=d{u}^r/d\tau +GM/r^2$. At a prospective radial turning point $u^r=0$, bounded outward proper acceleration $g$ permits $d{u}^r/d\tau \le g\sqrt{1-2GM/(c^{2}r)}-GM/r^2$. The equality $g=g_{\mathrm{hover}}$ defines a unique critical radius outside the horizon. A ship already falling inward cannot turn at or below it. The Newtonian proposed radius $\sqrt{GM/g}$ is strictly smaller and is therefore too late for reversal. A radius beyond the critical one is necessary, but braking must also remove the pre-existing inward velocity.